The luminosity distance-redshift relation up to second order in the Poisson gauge with anisotropic stress

Understand

We present the generalization of previously published results, about the perturbed redshift and the luminosity-redshift relation up to second order in perturbation theory, for the case of the Poisson gauge and in the presence of anisotropic stress.

• The results are therefore valid for general dark energy models and (most) modified gravity models.
• We use an innovative approach based on the recently proposed "geodesic light-cone" gauge.
• We then compare our finding with other results, which recently appeared in the literature, for the particular case of vanishing anisotropic stress.